Capacity of Multiple Antenna Gaussian Broadcast Channel at High SNR

The downlink problem in a wireless system with multiple transmit antennas and multiple users can be modeled by a multiple input multiple output Gaussian broadcast channel. The capacity region of this channel is still an open problem. Caire and Shamai [1] applied a technique known as "dirty-paper coding," due to Costa [2], to find an achievable region. It was later shown [3] that the maximum sum rate of this region is also the maximum possible sum rate. It is widely believed that this achievable region is in fact optimal. We attempt to show that this conjecture is true at high SNRs. We hope that solving this problem would give insights into the general problem.